2024-04-18T07:11:11Z
https://nagoya.repo.nii.ac.jp/oai
oai:nagoya.repo.nii.ac.jp:00026544
2023-01-16T04:29:21Z
312:313:314
Impossibility of Classically Simulating One-Clean-Qubit Model with Multiplicative Error
Fujii, Keisuke
87258
Kobayashi, Hirotada
87259
Morimae, Tomoyuki
87260
Nishimura, Harumichi
87261
Tamate, Shuhei
87262
Tani, Seiichiro
87263
The one-clean-qubit model (or the deterministic quantum computation with one quantum bit model) is a restricted model of quantum computing where all but a single input qubits are maximally mixed. It is known that the probability distribution of measurement results on three output qubits of the one-clean-qubit model cannot be classically efficiently sampled within a constant multiplicative error unless the polynomial-time hierarchy collapses to the third level [T. Morimae, K. Fujii, and J. F. Fitzsimons, Phys. Rev. Lett. 112, 130502 (2014)]. It was open whether we can keep the no-go result while reducing the number of output qubits from three to one. Here, we solve the open problem affirmatively. We also show that the third-level collapse of the polynomial-time hierarchy can be strengthened to the second-level one. The strengthening of the collapse level from the third to the second also holds for other subuniversal models such as the instantaneous quantum polynomial model [M. Bremner, R. Jozsa, and D. J. Shepherd, Proc. R. Soc. A 467, 459 (2011)] and the boson sampling model [S. Aaronson and A. Arkhipov, STOC 2011, p. 333]. We additionally study the classical simulatability of the one-clean-qubit model with further restrictions on the circuit depth or the gate types.
journal article
American Physical Society
2018-05-17
application/pdf
Physical Review Letters
20
120
200502
0031-9007
1079-7114
https://nagoya.repo.nii.ac.jp/record/26544/files/PhysRevLett120_200502.pdf
eng
https://doi.org/10.1103/PhysRevLett.120.200502
© 2018 American Physical Society